The rapid rise of Large Language Models (LLMs) has transformed multiple domains, from natural language processing to automated content generation. As they grow in size and complexity, this models accumulate capabilities that go beyond their main intended purpose. While extensive research has explored the degrees to which LLMs accidentally memorize their training data, including copyrighted material, little attention has been paid to their ability to memorise and recall out of distribution (OOD) data. In this work, we perform the first such study, introducing memorization on encrypted data (MED), a method designed to embed and retrieve encrypted data within LLMs, while preserving the LLM utility on its original tasks. MED can be used for multiple purposes: as a model watermarking mechanism, as a means to share secrets, or even as a data compression mechanism. We experiment with two encryption algorithms, Shift Cipher and AES, that generate data distributions significantly different from each other and from that used for training LLMs. We show that large encrypted text blocks can be memorized by LLMs without harming their regular performance, even when using cryptographically secure protocols like AES.